A reversible information hiding method and system based on wavelet domain compressed sensing image

Abstract

The application provides a reversible information hiding method and system based on wavelet domain compressed sensing images, and proposes a reversible information hiding method taking a compressed sensing file as a main body, selects HL and LH parts of a wavelet domain, reconfigures a sparse measurement area of compressed sensing and an embedding mode, fully retains sparsity of compressed sensing, and thus improves compression and reconstruction efficiency of compressed sensing; under the condition of realizing reversible information hiding, very low file increment and excellent visual quality are ensured.

Description

Technical Field

[0001] This invention belongs to the field of image compressed sensing technology, and particularly relates to a reversible information hiding method and system based on wavelet domain compressed sensing images. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Traditional information hiding methods, once embedded with secret information, destroy the carrier image, making it impossible to recover even after information extraction. However, for some sensitive fields, the carrier image still possesses significant value. Reversible information hiding technology can solve this problem. With the development of digital media in recent years, reversible information hiding technology has attracted increasing attention from scholars. Since Barton first defined the concept of reversible information hiding in 1997, the field has undergone rich development. Based on the image encoding, image-based reversible information hiding can be divided into two main categories: spatial domain and compression domain.

[0004] The core technologies of spatial domain-based reversible information hiding algorithms fall into three main categories: lossless compression, difference expansion, and histogram translation. Fridrich et al. first proposed a lossless compression-based reversible information hiding method, which provides embedding locations for secret information by compressing redundant data. To improve embedding capacity, Celik et al. proposed a least significant bit-based reversible information hiding method, compressing the redundant data of the carrier and embedding it as information. Tian proposed a difference expansion-based reversible information hiding method, which utilizes the correlation between pixels to embed secret information into the difference between adjacent pixels, but its over-reliance on the relationship between each pair of pixels results in a small hiding capacity. Histogram modification was first proposed by Ni et al., which represents the image as a histogram, then finds the peaks and zeros, and shifts the pixels located at these peaks and zeros to provide space for embedding secret data. Thodi et al. combined prediction error with histogram translation to construct a difference histogram for embedding, effectively improving the embedding performance. Ma et al. innovatively proposed a reversible information hiding method based on code division multiplexing. They used different orthogonal sequences to represent secret information and embedded it into the carrier. Utilizing the linear independence property of orthogonal vectors, the secret information can be overlapped and embedded. Under high embedding capacity, most embedded elements can cancel each other out without affecting extraction, effectively improving embedding capacity and image quality. Weng et al. improved the traditional prediction error expansion method by using K-means clustering to construct multiple sub-histograms and determining the embedding points through an improved cross-optimization algorithm, effectively improving computational speed while reducing distortion of the image carrying the secret. Wang et al. proposed a high-precision error prediction algorithm for reversible data hiding based on a ridge regression predictor, significantly improving prediction accuracy and embedding performance.

[0005] With the development of social networks, image transmission has largely shifted to compressed image transmission, leading to increased attention to reversible information hiding based on the compression domain. JPEG, as a classic compression method, boasts superior performance in both compression efficiency and image quality. Furthermore, compressed sensing, due to its outstanding compressed sampling and efficient image reconstruction, has also been favored by scholars since its inception. Current developments in compressed sensing theory demonstrate its wide range of applications, thus reversible information hiding based on JPEG images and compressed sensing has received significant attention in recent years. Reversible information hiding for JPEG images can be broadly categorized into three main methods: those based on modified quantization tables, those based on modified Huffman tables, and those based on modified quantized DCT coefficients. Methods based on modified quantization tables: In 2001, Fridrich et al. first proposed a reversible information hiding scheme that embeds secret information by modifying the quantization table and consequently the quantization coefficients. Chang et al. modified the Discrete Cosine Transform (DCT) coefficients to better preserve other quantization operations in JPEG compression, improving embedding capacity and visual effects. Methods based on modified Huffman tables: Mobasseri et al. proposed a JPEG reversible information hiding scheme based on modified Huffman tables, embedding secret information into entropy-decoded JPEG image data. Based on a modified Huffman map, Qiu et al. employed a code reordering-based embedding method to improve embedding capacity while maintaining image quality. Zhang et al. used a value transfer matrix to simulate ideal VLC replacement and further constructed an invertible map to balance embedding capacity and file increment. Qiu et al. optimized data hiding through variable-length code (VLC) mapping, combination, and permutation, proposing a relay-based algorithm to preprocess JPEG bitstreams, thereby effectively controlling file increment. Methods based on modified quantized DCT coefficients: Nikolaidis et al. embedded information by modifying the zero coefficients after quantization, achieving high image quality without considering file increment. Huang et al. performed adaptive selection based on the number of zero coefficients in the DCT block, embedding information into the positive and negative "1"s of the DCT coefficients, effectively suppressing file increment while maintaining image quality. Li et al. proposed a novel JPEG reversible information hiding scheme based on pairwise non-zero AC coefficient expansion. They constructed a two-dimensional histogram by combining every two adjacent non-zero AC coefficients to generate non-zero AC coefficient pairs (NACPs), and designed a two-dimensional invertible map to modify the non-zero coefficient pairs for data embedding. This approach ensured high image quality and low file increment. Chen et al. further improved this by pairing two non-zero coefficients with the same frequency in adjacent blocks to obtain more coefficient pairs with higher embedding efficiency. They also improved and optimized the coefficient pair mapping, further enhancing image quality and achieving even smaller file increments.It is undeniable that although these methods have been continuously improved in suppressing file increments, they still produce a significant increment to the original compressed file, affecting the transmission efficiency of the compressed file.

[0006] Compressed sensing, a novel theoretical method proposed in 2006 by Candes, Roberg, Donoho, and Tao, can perform compression simultaneously with sampling and accurately reconstruct the original signal with very few sample values. This offers a significant advantage over traditional signal processing methods that involve sampling first and then compressing. Due to its excellent compression performance, compressed sensing can significantly improve transmission speed and save storage space. Furthermore, since the main work of compressed sensing is concentrated at the reconstruction end, sampling and compression can be completed quickly, resulting in excellent compression speed. Therefore, reversible information hiding based on compressed sensing is gradually gaining attention in the field of information security. Information hiding work based on compressed sensing can be mainly divided into two categories: one is compressed sensing of secret information, and the other is compressed sensing of carrier data. In 2007, Sheikh et al. first attempted information hiding in the sparse domain using compressed sensing. They first performed sparse transformations on the image, found a suitable sparse domain, and compressed the sparse coefficients. Then, they used a measurement matrix to compress the information to be embedded and embedded it into the sparse domain data representation. After inverse transformation, the data was transmitted. The same sparse transformation was performed at the extraction end, and a compressed sensing recovery method was used to recover the watermark and image data. In 2011, Zhang et al. proposed a flexible watermark self-recovery algorithm combining compressed sensing. They compressed the watermark information using compressed sensing and then embedded the compressed watermark information into the carrier image. At the watermark extraction end, compressed sensing was used to reconstruct the watermark and the damaged image. All of the above methods require compressed sensing operations on the watermark information during embedding. Since the reconstruction of compressed sensing is irreversible, the extracted secret information cannot completely recover the original information. Therefore, the focus of information hiding work based on compressed sensing has shifted to the carrier data. In 2014, Claude et al. stopped using compressed sensing operations on the watermark information and instead hid it in the non-zero coefficients of the sparse domain of the signal. Furthermore, the embedding process differed from previous designs; instead, the non-zero coefficients were added to the secret information using addition. In 2016, Further research was conducted on this type of method. Instead of relying on compressed sensing for information embedding, they linearly encoded the data for compressed sensing measurements and embedded information into the measured values ​​after compressed sensing sampling. Furthermore, the principle of compressed sensing inherently provides encryption protection by using random or pseudo-random measurement matrices for linear sampling of the signal. Therefore, some scholars have focused on encryption characteristics when researching information hiding in compressed sensing. In 2016, Li et al. first proposed a reversible information hiding method based on block compressed sensing. This method uses a key-generated measurement matrix to sample the signal while simultaneously encrypting it. The encrypted data to be embedded is then embedded into the block compressed sensing image. During embedding, the boundary pixels of adjacent blocks are used to define block fluctuations, employing an inter-block embedding method. However, this method still has a high extraction error rate. In 2017, Zheng et al. further improved this method by separating the right and bottom edge pixels of each block, utilizing the adjacent blocks not used by Li et al., effectively increasing the embedding capacity. In 2018, Building upon their 2016 work, researchers further improved robustness by replacing the decoding end with an alternating direction multiplier method (ADMM) decoding algorithm. In 2020, A multi-level data anonymization method based on compressed sensing and reversible data hiding was proposed. This method encrypts and compresses the entire data using compressed sensing, while sensitive parts of the image are hidden within the compressed sensing encryption domain using reversible data hiding. First-level decryption decodes the compressed sensing encryption, revealing the image excluding the sensitive areas. Second-level decryption completely decrypts all image regions. If the sensitive areas are compromised, they can be recovered from the extracted information. However, the above methods primarily focus on using compressed sensing combined with information hiding for encryption or authentication, neglecting the importance of reversible information hiding based on compressed sensing files and overlooking the efficient compression characteristics and file increment issues of compressed sensing. High embedding capacity, good visual quality, and low file increment remain the main challenges for reversible information hiding in the compressed domain, especially regarding file increment. While most current reversible information hiding schemes in the compressed domain can guarantee good visual quality and high embedding capacity, addressing the issue of excessive file increment after embedding information in the compressed domain remains a critical challenge. Summary of the Invention

[0007] To overcome the shortcomings of the prior art, this invention provides a reversible information hiding method and system based on wavelet domain compressed sensing images. It proposes a reversible information hiding method with compressed sensing files as the main body, selecting the HL and LH parts of the wavelet domain, resetting the sparse measurement region and embedding method of compressed sensing, fully preserving the sparsity of compressed sensing, thereby improving the compression and reconstruction efficiency of compressed sensing; under the condition of achieving reversible information hiding, it ensures extremely low file increment and excellent visual quality.

[0008] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solution: a reversible information hiding method based on wavelet domain compressed sensing images, comprising:

[0009] The original image is acquired and decomposed into mid-frequency, low-frequency, and high-frequency components using wavelet transform.

[0010] The intermediate frequency is downsampled using point / fork set sampling, and the low-frequency and high-frequency components are fully sampled.

[0011] The sampled data is quantized and encoded, and then used as a secret information carrier to embed secret information, thus obtaining compressed sensing image compressed data.

[0012] After performing a reverse embedding operation on the compressed sensing image data, the secret information is extracted. The extracted compressed sensing quantized data is then dequantized and the point / fork set is reset to obtain the imaging image.

[0013] A second aspect of the present invention provides a reversible information hiding system based on wavelet domain compressed sensing images, comprising:

[0014] Wavelet decomposition module: Decomposes the original image using wavelet transform, dividing it into mid-frequency, low-frequency, and high-frequency components;

[0015] Sampling module: performs point / fork set downsampling on the intermediate frequency and full sampling on the low frequency and high frequency components;

[0016] Compressed sensing module: After quantizing and encoding the sampled data, it embeds secret information as a carrier to obtain compressed sensing image data;

[0017] Reconstruction module: After performing a reverse embedding operation on the compressed sensing image data, the secret information is extracted. The extracted compressed sensing quantized data is then dequantized and the point / fork set is reset to obtain the imaging image.

[0018] Thirdly, embodiments of the present invention provide a computer device, including: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform the steps of a reversible information hiding method based on wavelet domain compressed sensing images as described in the first aspect above.

[0019] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, performs the steps of a reversible information hiding method based on wavelet domain compressed sensing images as described in the first aspect above.

[0020] The above one or more technical solutions have the following beneficial effects:

[0021] In this invention, a reversible information hiding method based on compressed sensing files is proposed. The HL and LH parts of the wavelet domain are selected, and the sparse measurement region and embedding method of compressed sensing are reset to fully preserve the sparsity of compressed sensing, thereby improving the compression and reconstruction efficiency of compressed sensing. Under the condition of achieving reversible information hiding, extremely low file increment and excellent visual quality are guaranteed.

[0022] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0023] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0024] Figure 1 This is a flowchart of the JPEG compression process in Embodiment 1 of the present invention;

[0025] Figure 2 This is a schematic diagram of the Zig-zag encoding scanning sequence in Embodiment 1 of the present invention;

[0026] Figure 3 This is a schematic diagram of compressed sensing measurement in Embodiment 1 of the present invention;

[0027] Figure 4 This is a schematic diagram of the overall structure of reversible information hiding based on wavelet domain compressed sensing images in Embodiment 1 of the present invention;

[0028] Figure 5 This is a schematic diagram of the dimensionality reduction sampling method in Embodiment 1 of the present invention;

[0029] Figure 6 This is a diagram of the end-to-end compressed sensing framework in Embodiment 1 of the present invention;

[0030] Figure 7(a) is a schematic diagram of the average size of compressed sensing files under different wavelet bases in Embodiment 1 of the present invention;

[0031] Figure 7(b) is a schematic diagram of the image quality of different wavelet basis dimensionality reduction compressed sensing reconstruction in Embodiment 1 of the present invention;

[0032] Figure 8(a) is a schematic diagram of the file increment after embedding the Baboon compressed sensing image file in Embodiment 1 of the present invention;

[0033] Figure 8(b) is a schematic diagram of the file increment after embedding the Boots compressed sensing image file in Embodiment 1 of the present invention;

[0034] Figure 8(c) is a schematic diagram of the file increment after Peppers compressed sensing image file embedding in Embodiment 1 of the present invention;

[0035] Figure 8(d) is a schematic diagram of the file increment after embedding the Lena compressed sensing image file in Embodiment 1 of the present invention;

[0036] Figure 9 This is a schematic diagram showing the average file increment after embedding different images in Embodiment 1 of the present invention;

[0037] Figure 10(a) is a schematic diagram of file increment after different image embeddings under Baboon two-dimensional embedding in Embodiment 1 of the present invention;

[0038] Figure 10(b) is a schematic diagram of file increment after different image embedding under Boats two-dimensional embedding in Embodiment 1 of the present invention;

[0039] Figure 10(c) is a schematic diagram of file increment after different image embedding under Peppers two-dimensional embedding in Embodiment 1 of the present invention;

[0040] Figure 10(d) is a schematic diagram of file increment after different image embeddings under Lena two-dimensional embedding in Embodiment 1 of the present invention;

[0041] Figure 11 This is a schematic diagram of the SSIM mean of the image carrying the secret and the original image in Embodiment 1 of the present invention. Detailed Implementation

[0042] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0043] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0044] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0045] Example 1

[0046] For an explanation of the principles of JPEG, such as Figure 1 As shown, the Joint Image Experts Group (JPEG) is a lossy compression algorithm based on Discrete Cosine Transform (DCT). The JPEG compression process mainly includes three parts: Discrete Cosine Transform, quantization, and encoding.

[0047] Regarding the Discrete Cosine Transform (DCT): The DCT transforms the spatial domain to the frequency domain, concentrating energy and facilitating subsequent removal of high-frequency components. In JPEG compression, the image is first divided into 8×8 blocks, and then each block undergoes a Discrete Cosine Transform (DCT). After the DCT, most of the image information is concentrated in the upper left corner. For a pixel f(i,j), the DCT transforms it into F(u,v). The specific DCT formula and inverse transform are as follows:

[0048]

[0049]

[0050] For an N×M dimensional image, f(i,j) represents the pixel before transformation, u=0,1,2…N-1. V=0,1,2…M-1, when u=0, C(u)=1 / √2, when u≠0, C(u)=1; when v=0, C(v)=1 / √2, when v≠0, C(v)=1.

[0051] Quantization is the process of discarding high-frequency coefficients after obtaining the DCT transform coefficients. JPEG compression efficiency is controlled by the selection of the quantization table. Quantized DCT coefficients become integers, which cannot be accurately recovered during decoding. Therefore, the quantization process is lossy, which is the main reason for the degradation of image quality.

[0052] Regarding encoding: The quantized coefficients are encoded in two categories. The first category consists of the elements at position (0,0) in each 8×8 block, i.e., the DC coefficients (Direct Current components), representing the average value of each block. In JPEG, the DC components are encoded separately. Since the DC coefficients of any two adjacent 8×8 blocks differ very little, differential coding (DPCM) is used for them to improve the compression ratio. The second category consists of the remaining 63 coefficients in each 8×8 block, i.e., the AC coefficients. Run-Length Encoding (RLE) is used for these. To ensure that low-frequency components are arranged first and high-frequency components are arranged last, and to group the "0" coefficients together as much as possible, these 63 AC coefficients are arranged in a Zig-zag scan order, such as... Figure 2 As shown in the image. After this, Huffman coding is used to obtain the final compressed data.

[0053] However, reversible information hiding in JPEG images is based on DCT transform. As the amount of embedded secret data increases, the file size increases significantly. Furthermore, at the image compression end, the compression effect of DCT transform deteriorates further with increasing compression levels, leading to a further deterioration in image quality. In contrast, reversible information hiding based on wavelet domain compressed sensing images can find a suitable sparse basis in the wavelet domain for dimensionality reduction compression, effectively improving the image quality at higher compression ratios and facilitating the transmission of large amounts of information over limited channels.

[0054] like Figure 3 As shown, the general process of compressed sensing is to represent the original signal as a compressible sparse signal on a certain transform basis, and then use an observation matrix to map the high-dimensional sparse signal to a low-dimensional space. If this observation matrix satisfies the condition that it is unrelated to the transform domain, that is, to ensure that the projection contains enough information of the original signal, then the original signal can be reconstructed with a high probability through an optimization problem using a small number of projections in these low-dimensional spaces.

[0055] Sparse representation is a prerequisite for compressed sensing. Accurate reconstruction in compressed sensing requires the signal to possess sparsity. For an N-dimensional signal x, if only a small number of elements are non-zero, then the signal is a sparse signal. Most signals in nature are not sparse, but a sparse basis ψ can be found such that the signal is represented on this basis as α = ψx. If α satisfies the above condition, then this type of signal is also called a sparse signal. There are many ways to choose a sparse basis, such as the Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT), and Fast Fourier Transform (FFT) commonly used in digital image processing, all of which can be used to perform sparse transformations on images. The measurement process of compressed sensing is essentially the process of compressed sampling. For an N-dimensional signal x, after passing through an M-dimensional measurement matrix... Dimensional reduction projection yields the M-dimensional measurement value y, i.e. Where x = ψα, M << N.

[0056] Among them, the perception matrix The original N-dimensional sparse signal α is projected onto M dimensions, thus achieving dimensionality reduction and compression. Compressed sensing theory proves that when the sensing matrix Θ satisfies the Restricted Isometry Property (RIP) property, it can be solved... The inverse problem is used to reconstruct the original signal x. Mathematically, this is expressed as: α = min||α||0s.ty = Θα, where ||||0 represents the L0 norm. However, solving the L0 norm is usually an NP-hard problem. But under certain conditions, the L0 norm problem can be transformed into an L1 norm problem, i.e.: min||α||1s.ty = Θα. Because minimizing the L1 norm is a convex optimization problem, the L1 norm problem can be transformed into a linear programming problem. Therefore, the L0 norm is used to approximate the norm.

[0057] Wavelet transform is an important development following Fourier transform. A wavelet can be understood as a very small wave, essentially a function. Not all small waves can be called wavelets; a wavelet must exhibit alternating positive and negative wave characteristics and have a zero DC component. Furthermore, the energy of a wavelet is finite, mainly concentrated around a certain moment, and gradually decays with time or distance. The definition of a wavelet is: for any function ψ(t), if ψ(t)∈L 2 (R), meaning the function is square-integrable when it satisfies:

[0058]

[0059] Here, ψ(t) is called the wavelet function. ψ(t) fluctuates up and down as t changes, hence the term wavelet. After translation and scaling, ψ(t) yields a family of functions:

[0060]

[0061] 'a' is called the scaling parameter, or scaling parameter, and 'b' is called the displacement parameter. Thus, we have the following one-dimensional continuous wavelet transform:

[0062]

[0063] Through the above transformation, the one-dimensional signal is converted from the time domain to the wavelet domain, which consists of time and scale. This gives the wavelet transform multi-scale characteristics. By adjusting the scaling factor and translation factor, the signal can be observed at different scales.

[0064] Digital image processing involves two-dimensional signals, and the corresponding wavelet transform needs to be extended from one-dimensional to two-dimensional. The two-dimensional continuous wavelet basis function is defined as:

[0065]

[0066] Therefore, the two-dimensional continuous wavelet transform can be expressed as:

[0067]

[0068] The Haar wavelet is the earliest wavelet used for wavelet analysis, generated by translating and scaling basic wavelets, and it is also the simplest wavelet.

[0069] This embodiment discloses a reversible information hiding method based on wavelet domain compressed sensing images, including:

[0070] Step 1: Obtain the original image and decompose it using wavelet transform, dividing it into mid-frequency, low-frequency, and high-frequency components;

[0071] Step 2: Perform point / fork set downsampling on the intermediate frequency, and perform full sampling on the low frequency and high frequency components;

[0072] Step 3: After quantizing and encoding the sampled data, embed the secret information as a carrier to obtain compressed sensing image data;

[0073] Step 4: After performing a reverse embedding operation on the compressed sensing image data, the secret information is extracted. The extracted compressed sensing quantized data is then dequantized and the point / fork set is reset to obtain the imaging image.

[0074] In step 1 of this embodiment, the original image is subjected to wavelet transform, and then the wavelet decomposition coefficients are sampled. The wavelet coefficients consist of four parts, namely HH\LH\HL\LL.

[0075] like Figure 4 As shown, at the transmitting end, the image is first represented in the wavelet domain. After separating the HL, LH, HH and LL of the image, the intermediate frequency (HL, LH) is downsampled by point / fork set, and the low frequency (LL) and high frequency (HH) data are fully sampled. The intermediate frequency data is used as the carrier of secret information. The high frequency is not embedded, but it is used as the reconstruction information for image reconstruction, just like the intermediate frequency information.

[0076] After sampling, the data is quantized and encoded, and then used as a carrier of secret information for embedding. The embedding process first uses the mid-frequency region data as the operation area and performs histogram scanning to obtain the first and second peak points. The length of the secret information is compared to select single-peak embedding or double-peak embedding. After entropy encoding and other operations, compressed sensing data is obtained.

[0077] After receiving compressed sensing data at the receiving end, entropy decoding is performed to extract intermediate frequency (IF) and high / low frequency quantized data. Inverse embedding operation is performed on the IF data to extract secret information. After extraction, the compressed sensing quantized data is dequantized and the point / fork set is reset. Then, the compressed sensing reconstruction algorithm can be used to reconstruct the compressed sensing image from the data to obtain the imaging image.

[0078] The quantization scheme employs the uniform quantization method, a commonly used scalar quantization approach. This method maps each sampled value y to its corresponding codeword Q(y), as defined below:

[0079]

[0080]

[0081] Where y is each sampled value, μ is the average of the sampled values, s represents the quantization step size, and L is a positive integer that determines the quantization range. Dequantization is defined as follows: R = Q(y)s + μR, where R represents the dequantized sampled value.

[0082] Most signals in real life do not satisfy the sparsity property, especially image signals. Dimensionality reduction compression in compressed sensing requires sparse bases. Often, measurements relying on sparse bases can have their reconstructed image quality affected by even small modifications; therefore, the choice of sparse base and measurement method is not arbitrary. Considering the advantage of compressed sensing systems—high compression performance and image quality at high compression rates—wavelet transform is chosen to construct sparse representations instead of discrete cosine transform. Previous image compression studies have shown that at high compression rates, wavelet transform outperforms discrete cosine transform, meaning it provides higher quality images at lower bit rates compared to discrete cosine transform.

[0083] When constructing sparse representations using wavelet transform, the choice of wavelet basis functions is crucial, as different wavelet bases directly affect the image compression performance. Daubechies wavelets possess characteristics such as orthogonality, tight time-frequency support, and high regularity, exhibiting high sensitivity to non-stationary signals and making them one of the most widely used wavelet bases. The larger the order N of the Daubechies wavelet function, the longer the filter length and the better the performance. Among bioorthogonal wavelets, the Daubechies 9 / 7 wavelet exhibits the best coding performance; therefore, the Daubechies 9 / 7 wavelet basis is chosen to construct the sparse representation. The Daubechies wavelet is defined as follows: This represents the binomial coefficient.

[0084]

[0085] Wavelet transform can be understood in conjunction with Fourier transform. Fourier transform decomposes the original function using a series of sine and cosine functions of different frequencies, yielding the coefficients of the original function at different frequencies of sine and cosine. Wavelet transform decomposes the original function using a series of wavelets of different scales, yielding the coefficients of the original function at different wavelet scales. Different wavelets are decomposed through translation and scaling transformations; translation is used to obtain the time characteristics of the original function, while scaling is used to obtain the frequency characteristics.

[0086] In step 2 of this embodiment, a new compressed sensing sampling method is explored in the wavelet coefficient domain, so that the final image can balance the performance of image quality, embedding capacity and compression efficiency.

[0087] For the original image, a global wavelet transform is applied, and the low-frequency coefficients after the wavelet transform, i.e., the LL part, are fully preserved because this part contains the most important image information. Meanwhile, the HH region is also very sensitive to image transformations, so the dimensionality reduction and embedding operations are ultimately limited to the mid-frequency region. For the HL and LH regions, discarding either one means losing image details along the wavelet decomposition direction, which is not conducive to high-quality image restoration; complete preservation is not conducive to efficient compression. Therefore, this embodiment combines point sets and cross sets to adopt a new sampling method, specifically implemented as follows: Figure 5 As shown, the mid-frequency coefficients are sampled, completely preserving the coefficients in the LL and HH regions, and ensuring that the coefficients are not modified. That is, the LL and HH regions are not embedded, so the coefficients will not change due to embedding. Then, the coefficients of the point set or cross set of LH and HL are preserved. Figure 5 The sampling method shown is as follows: for the LH and HL region data, if the data in the first row and first column is sampled, then the data in the first row and second column is not sampled, and then the data in the first row and third column is sampled, that is, intermittent sampling. At the same time, the data in the second row and first column is not sampled, which ensures that the sampled data are not adjacent in the horizontal and vertical directions. It is similar to the distribution of a black and white checkerboard. Either only the black area data on the checkerboard is selected, or only the white area data is selected.

[0088] In step 3 of this implementation, a reversible information hiding algorithm based on histogram translation is used to embed the secret data into the quantized compressed sensing measurement coefficients. For the quantized coefficients of compressed sensing, corresponding to the four wavelet transform coefficients LL, HH, HL, and LH, the LL part contains the main information of the image and its coefficients are much larger than the other two parts. Therefore, even a very small change in this part will seriously affect the quality of the reconstructed image, so this part is classified as a non-embedding region. For the HL and LH parts, since the coefficients after point set dimensionality reduction sampling and quantization in this embodiment contain both horizontal and vertical detail information of the image, and their coefficient distribution conforms to a Labras distribution, these coefficients have a high embedding capacity. Furthermore, changes to this part of the data have a relatively small impact on the reconstructed image. Therefore, the sampled data of the HL and LH parts are classified as embeddable regions. The specific embedding operation is as follows:

[0089]

[0090]

[0091] In the above formula D represents the embedded compressed sensing data. i This represents the initial compressed sensing data, which is the data obtained after dimensionality reduction sampling and quantization of the intermediate frequency coefficients. A represents the maximum peak value (excluding zero). The histogram represents the number of identical values. If the x-axis coordinate of the maximum peak value in the histogram is 4, it indicates that the number of data points with a value of 4 is the largest, and therefore the value of A represents 4. i ∈{0,1} represents the secret information to be embedded. V(x) is a function designed to achieve information embedding and reversible extraction. That is, to explain the meaning of V(A) in formula (9), V(x) represents the usage of V(A) in formula (9).

[0092] During the embedding process, the sparsity of compressed sensing is fully utilized while avoiding zero-coefficient embedding to ensure file compression. Therefore, even after data embedding is completed, the compressed sensing data still maintains high sparsity. In addition, the amount of data that needs to be modified is controlled within half. Only the histogram on the zero-coefficient side needs to be moved for embedding, thereby achieving low-incremental compressed sensing reversible information hiding embedding and ensuring the quality of the original image.

[0093] In addition, to increase the embedding capacity while balancing file increment, an adaptive embedding adjustment scheme is added. During each embedding operation, when scanning the coefficients of the HL / LH portion, the following operation is performed:

[0094]

[0095]

[0096] In step 4 of this embodiment, the corresponding information extraction and image restoration (reverse embedding operation) formulas are expressed as formulas (11) and (12). D′ represents the secret information extracted from the i-th pixel. i This represents the numerical restoration of the extracted pixels.

[0097]

[0098]

[0099] like Figure 5 As shown, taking the HL region as an example, point set sampling, at the compressed sensing reconstruction end, that is, after extracting the secret information, requires compressed sensing restoration of the image. Make full use of the feature structure of the signal, further mine the prior knowledge of the image, and improve the reconstruction effect of compressed sensing. Utilize the nonlocal self-similarity of the image, and adopt the Nonlocal Low Rank Regularization (NLR_CS) compressed sensing reconstruction method, which regularizes the compressed sensing restoration through block grouping and low-rank approximation.

[0100] First, the wavelet coefficients obtained from the measured values ​​(i.e., the point set and the cross set) are used to obtain the initial estimate Ix of the image to be reconstructed by a standard compressed sensing reconstruction algorithm (such as the wavelet reconstruction method). Then, block matching is performed on the initial estimated image Ix.

[0101] Block matching is performed on the initially estimated image Ix, specifically including: utilizing non-local self-similarity, for each sample block xi, finding similar blocks Xij in its K-neighborhood search box, satisfying... Let Xi represent the set of blocks similar to the sample block. After grouping, the set of similar blocks corresponding to each sample block is denoted as Xi = [xi1, xi2, ..., xin]. Xi may contain noise, i.e., Xi = Li + Wi, where Li is a low-rank matrix and Wi is a noise matrix. Li can then be solved using an optimization problem.

[0102]

[0103]

[0104] in, A matrix is ​​composed of a set of similar blocks. The variance representing Gaussian noise, ε represents the measurement matrix in the fundamental theory of compressed sensing, λ is a very small constant, and λ represents a suitable regularization parameter.

[0105] After performing the reverse embedding operation on the compressed sensing image data (Formula (11) and Formula (12)), the secret information is extracted, that is, histogram extraction. The coefficients after dequantization are scanned. If the coefficient is equal to the peak point, the secret information is extracted as 0. If the coefficient is equal to the peak point + 1, the secret information is extracted as 1. The extracted compressed sensing quantized data is dequantized and the point / fork set is reset to obtain the imaging image.

[0106] like Figure 6 A basic end-to-end compression-aware file compression and reconstruction framework is presented. It transforms the compressed data from real number arrays into bit or byte sequences, thus achieving a truly complete compression-aware compression method.

[0107] To verify the advancement of the above scheme, relevant experiments were designed. Specifically, for the embedding end, the following operations were performed: 1. Discrete wavelet transform was applied to the original image to obtain a sparse representation, separating the image into four parts: LL, HL, LH, and HH. 2. Dimensionality reduction measurement of HL and LH was performed using the point / difference set method. After completion, the dimensionality-reduced data and LL and HH were quantized. Here, since vector quantization does not have a significant advantage over scalar quantization in compressed sensing, a uniform quantizer in the scalar quantizer was used for ease of processing. 3. The quantized data was divided into blocks for embedding operations, and an adaptive embedding operation was added. 4. The embedded data was losslessly encoded to generate the final compressed sensing image file.

[0108] After receiving the carrier image file, the receiving end can perform two types of operations: First, without extracting the secret information, it directly decodes and dequantizes the carrier image file, then reconstructs the obtained data using compressed sensing low-rank regularization to obtain an imaging file that does not affect the image's visual quality. Second, it extracts the secret information during the decoding and dequantization process of the received carrier image file. After the secret information is extracted, the carrier data can be recovered losslessly. Using the recovered data for compressed sensing low-rank regularization reconstruction yields a higher-quality imaging file.

[0109] The extraction process involves the following steps: 1. First, entropy decoding is performed on the secret compressed sensing image file to obtain quantized compressed sensing sampling data. 2. The decoded data is then divided into embedded and non-embedded regions according to wavelet region classification. For the embedded region data, the inverse operation of the embedding method is used as described above to extract the secret information m and recover the carrier data. m is saved, and then the recovered carrier data is dequantized to obtain the initial approximate compressed sensing measurement value y'. 3. The measurement value y' is reset using point-fork sets and LL and HH, and then the image is initially recovered from the reset measurement value. 4. Finally, image recovery is performed through compressed sensing low-rank reconstruction.

[0110] After determining that wavelet transform is used as the sparse representation for compressed sensing, the results of wavelet transform vary depending on the different wavelet basis functions, which in turn affects the size and quality of image compression. The selection criteria for wavelet bases generally include the following: 1. Support length: The longer the support length, the longer the computation time required, and the more high-amplitude wavelet coefficients. Too long a support length can cause boundary problems, while too short a support length results in a low vanishing moment, which is not conducive to the concentration of signal energy. Therefore, a wavelet basis with an appropriate support length needs to be selected. 2. Symmetry: In image processing, wavelets with symmetry can effectively avoid phase distortion. 3. Vanishing moment: Applying vanishing moment conditions to the basic wavelet ensures as many zero coefficients as possible and as few non-zero coefficients as possible, which is beneficial for data compression and noise reduction. The larger the vanishing moment, the more wavelet coefficients become zero. 4. Regularity: Good regularity allows the wavelet transform to achieve better smoothing effects in signal or image reconstruction, reducing the visual impact of errors. However, in general, the support length changes with regularity, thus affecting the computation time more significantly. Therefore, before selecting wavelet bases for experiments, commonly used wavelet bases were screened based on these properties to observe their different characteristics in reconstruction and compression. Based on this, experiments were conducted on images from the MISC database to test the impact of different wavelet bases on compressed file size and image reconstruction quality under compressed sensing. Figure 7a , Figure 7b The experimental results clearly show that, at the same sampling rate, different wavelet bases produce compressed image files of different sizes and with varying reconstructed image quality. The sparse representation under the Haar wavelet base results in the largest compressed file size; the sparse representation under the Bior 2.4 wavelet base leads to the worst image reconstruction quality; however, the sparse representation under the DB9 / 7 wavelet base results in the smallest compressed file size and the highest image quality. Therefore, the DB9 / 7 wavelet base was ultimately chosen as the sparse representation for compressed sensing signals.

[0111] In the embedding experiment, 0 / 1 secret information strings of different lengths were randomly generated. To demonstrate the generalization ability of the method, images from the MISC image database were embedded, such as... Figures 8(a)-8(d) Examples of images from this database are shown: Baboon, Boats, Lena, and Peppers. The embedding information length is controlled between 0 and 15000 bits, with intervals of 1000 bits. The incremental changes in compressed files and the PSNR effect after embedding compared to uncompressed files are observed. Furthermore, to better demonstrate the superiority of the proposed method, the experimental results are compared with two state-of-the-art reversible information hiding methods on JPEG files.

[0112] Figure 9 a- Figure 9Figure d shows the file increment changes for each of the four embedded images (Baboon, Boats, Peppers, and Lena, in that order). It can be seen that images with complex textures have higher file increments for the same embedding size. For JPEG files, the proposed method has smaller file increments for the same embedding size, which is beneficial for improving file transmission efficiency. Figures 10(a)-10(d) The average results of file increment after embedding are shown for different images in the MISC database.

[0113] On the other hand, (Li N, Huang F. Reversible data hiding for JPEG images based on pairwise nonzero AC coefficient expansion[J]. Signal Processing, 2020, 171: 107476.) uses two-dimensional histogram embedding, which has significant advantages compared to traditional one-dimensional histogram embedding. Although the method we used above already has advantages in file increment, in order to better demonstrate the dimensionality reduction and compression performance of our proposed method, we also conducted experiments using a two-dimensional embedding method. During the embedding process, we adjusted the carrier data so that it was linearly transformed into integers near zero during embedding, similar to (Yamac M, Dikici) Similar to the mapping method in Sankur B. Hiding data in compressive sensed measurements: A conditionally reversible data hiding scheme for compressively sensed measurements[J]. Digital Signal Processing, 2016, 48: 188-200., we compared the embedding effects.

[0114] like Figure 11 As shown, the two-dimensional histogram embedding methods used in the embedding process are Baboon, Boats, Peppers, and Lena, in that order. The method presented in this paper has a more significant advantage in terms of file increment.

[0115] In addition, we conducted comparative experiments on image quality, using SSIM (Structural Similarity) as a measure of image quality. We compared our proposed method with the efficient JPEG reversible information hiding method, comparing the structural similarity between the embedded image and the original image for each method. Figure 12 shows the average SSIM results for four images with different embedding levels.

[0116] As the embedding capacity increases, the reduction in SSIM (Structural Similarity Simplification) between the embedded JPEG image and the initial uncompressed image becomes increasingly significant. Because compressed sensing performs initial image reconstruction at the imaging end and secondary reconstruction and normalization through similar image regions, the reconstruction estimation of the original image at the imaging end is less sensitive to the influence of the embedding capacity. Therefore, the decay of structural similarity with increasing capacity is slowed down. Experimental results on image quality show that the proposed method effectively suppresses file increment while maintaining image quality nearly comparable to the JPEG reversible information hiding method, thus ensuring high image quality.

[0117] Therefore, the above experiments fully demonstrate that the proposed method not only has a significant advantage in terms of file increment but also ensures high image visual quality. This further proves the advancement of the proposed method, which can effectively suppress file increment of transmitted image files and improve transmission and storage efficiency. Especially in today's highly developed social networks, the proposed method effectively improves the transmission efficiency of transmitted data. At the same time, it ensures high-quality visual effects of transmitted images under specific conditions.

[0118] Example 2

[0119] The purpose of this embodiment is to provide a computing device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the above-described method.

[0120] Example 3

[0121] The purpose of this embodiment is to provide a computer-readable storage medium.

[0122] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps of the above method.

[0123] Example 4

[0124] The purpose of this embodiment is to provide a reversible information hiding system based on wavelet domain compressed sensing images, including:

[0125] Wavelet decomposition module: acquires the original image and decomposes it using wavelet transform, dividing it into mid-frequency, low-frequency, and high-frequency components;

[0126] Sampling module: performs point / fork set downsampling on the intermediate frequency and full sampling on the low and high frequency components;

[0127] Compressed sensing module: After quantizing and encoding the sampled data, it embeds secret information as a carrier to obtain compressed sensing image data;

[0128] Reconstruction module: After performing a reverse embedding operation on the compressed sensing image data, the secret information is extracted. The extracted compressed sensing quantized data is then dequantized and the point / fork set is reset to obtain the imaging image.

[0129] The steps and methods involved in the apparatuses of Embodiments 2, 3, and 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0130] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0131] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A reversible information hiding method based on wavelet domain compressed sensing images, characterized in that, include: The original image is acquired and decomposed into mid-frequency, low-frequency, and high-frequency components using wavelet transform. Point / fork set downsampling is performed on the intermediate frequency, and full sampling is performed on the low frequency and high frequency components. The point / fork dimensionality reduction sampling method is as follows: for the regional data of the intermediate frequency, if the data in the first row and first column is sampled, then the data in the first row and second column is not sampled, and then the data in the first row and third column is sampled, that is, intermittent sampling. At the same time, the data in the second row and first column is not sampled, and so on. The sampled data is quantized and encoded, then used as a secret information carrier for secret information embedding to obtain compressed sensing image data. During each embedding operation, an adaptive embedding adjustment is added, specifically: Scan the coefficients of the intermediate frequency component, read the maximum peak point and record the embedding capacity; If the embedding capacity is not less than the length of the secret information to be embedded, then the secret information is embedded into the compressed sensing compressed data; Otherwise, record the second peak point and the embedding amount, sequentially scan the i-th value in the compressed sensing data, move the compressed sensing data bidirectionally to both sides of 0, and move the first peak and the second peak for sub-embedding; After performing a reverse embedding operation on the compressed sensing image data, the secret information is extracted. The extracted compressed sensing quantized data is then dequantized and the point / fork set is reset to obtain the image. Specifically, the dequantization and point / fork set reset operations on the extracted compressed sensing quantized data are performed as follows: First, each sample value is dequantized. Then, the original wavelet transform coefficient matrix is ​​set to all zeros. The dequantized coefficients are then filled into the zero coefficient matrix row by row, ensuring that they are input at intervals. That is, if the first coefficient is filled into the first empty space in the i-th row of the matrix, the second coefficient is filled into the third position.

2. The reversible information hiding method based on wavelet domain compressed sensing images as described in claim 1, characterized in that, The sampled data in the intermediate frequency range is categorized into embeddable regions, and the embedding process is implemented as follows: in, This represents the embedded compressed sensing data. This represents the initial compressed sensing data. This represents the maximum peak value excluding zero. This represents the secret information to be embedded.

3. The reversible information hiding method based on wavelet domain compressed sensing images as described in claim 1, characterized in that, The extraction of secret information and image restoration after the compressed sensing image compressed data undergoes inverse embedding operation are as follows: in, This represents the embedded compressed sensing data. This represents the initial compressed sensing data. This represents the maximum peak value excluding zero. This represents the secret information to be embedded. Representative from the first Secret information extracted from bit pixels This represents the numerical restoration of the extracted pixels.

4. A reversible information hiding system based on wavelet domain compressed sensing images, characterized in that, include: Wavelet decomposition module: Decomposes the original image using wavelet transform, dividing it into mid-frequency, low-frequency, and high-frequency components; Sampling module: performs point / fork set downsampling on the intermediate frequency, and performs full sampling on the low frequency and high frequency parts; the point / fork dimensionality reduction sampling method is as follows: for the regional data of the intermediate frequency, if the data in the first row and first column is sampled, then the data in the first row and second column is not sampled, and then the data in the first row and third column is sampled, that is, intermittent sampling, while the data in the second row and first column is not sampled, and so on; Compressed sensing module: Quantizes and encodes the sampled data, then embeds it as a secret information carrier to obtain compressed sensing image data; during each embedding operation, an adaptive embedding adjustment is added, specifically: Scan the coefficients of the intermediate frequency component, read the maximum peak point and record the embedding capacity; If the embedding capacity is not less than the length of the secret information to be embedded, then the secret information is embedded into the compressed sensing compressed data; Otherwise, record the second peak point and the embedding amount, sequentially scan the i-th value in the compressed sensing data, move the compressed sensing data bidirectionally to both sides of 0, and move the first peak and the second peak for sub-embedding; Reconstruction Module: After performing a reverse embedding operation on the compressed sensing image data, the secret information is extracted. The extracted compressed sensing quantized data is then dequantized and the point / fork set is reset to obtain the image. Specifically, the dequantization and point / fork set reset operations are performed on each sample value. Then, the original wavelet transform coefficient matrix is ​​set to all zeros. The dequantized coefficients are then filled into the zero coefficient matrix row by row, ensuring that they are input at intervals. That is, if the first coefficient is filled into the first empty space in the i-th row of the matrix, the second coefficient is filled into the third position.

5. A computer device, characterized in that, include: The computer device includes a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform the steps of a reversible information hiding method based on wavelet domain compressed sensing images as described in any one of claims 1 to 3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of a reversible information hiding method based on wavelet domain compressed sensing images as described in any one of claims 1 to 3.

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